Broad stopband filters are proposed, based on multilayer electromagnetically induced transparency (EIT) metamaterial structures. The single EIT metamaterial consists of a U-shaped resonator and a strip on a polyimide substrate. The EIT-like spectral feature is firstly utilized to achieve stopband filters by properly coupling two layers of EIT structure. Influences of different rotation angles on the transmission properties of the two-layer EIT structure are investigated. It is found the wider low-transmission band can be obtained for the Transverse Magnetic (TM) polarization when the two EIT metal structures are vertical to each other. Furthermore, the bandwidth of the stopband can be controlled by increasing layers of the EIT structures with the proper architectural design. The design using a coupling effect of multi EIT-like resonances in the metamaterial would provide a new method for broad stopband filters in highly integrated optical circuits.